摘要翻译：
Chambert-Loir对a上的abelian变体a的闭d维子变体X和正则度量化线丛L在与a相关的Berkovich解析空间上引入了关于地面场离散估值的测度$C_1(L_X)^{\wedge d}$。本文利用凸几何给出了这些规范测度的显式描述。我们使用了与a的雷诺扩张和Mumford构造有关的热带化的一个推广。所得结果对小点的等分布有一定的应用。
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英文标题：
《Non-archimedean canonical measures on abelian varieties》
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作者：
Walter Gubler
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  For a closed d-dimensional subvariety X of an abelian variety A and a canonically metrized line bundle L on A, Chambert-Loir has introduced measures $c_1(L|_X)^{\wedge d}$ on the Berkovich analytic space associated to A with respect to the discrete valuation of the ground field. In this paper, we give an explicit description of these canonical measures in terms of convex geometry. We use a generalization of the tropicalization related to the Raynaud extension of A and Mumford's construction. The results have applications to the equidistribution of small points.
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PDF链接：
https://arxiv.org/pdf/0801.4503